GATE EC 2017 Set 1 — Question 64
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?
Correct answer
(A) 56
Solution
The total number of people in the group is 6. The total number of possible subsets (subgroups) that can be formed from a set of 6 people is .To find the number of subgroups that have at least one Indian, we can subtract the number of subgroups that contain no Indians from the total number of subgroups.A subgroup contains no Indians if it is formed entirely from the 3 Chinese people. The number of such subgroups is .Therefore, the number of subgroups containing at least one Indian is:Note: Even if we consider only non-empty subgroups, the result remains the same because the empty set is excluded from both counts ().
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